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How many 3- digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7 if no digit is repeated?

Q.3.    How many 3-digit even numbers can be made using the digits

          1, 2, 3, 4, 6, 7, if no digit is repeated?
         

         

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3-digit even numbers can be made using the digits  1, 2, 3, 4, 6, 7, if no digit is repeated.

The unit place can be filled in 3 ways by any digits from 2,4 or 6.

The digit cannot be repeated in 3-digit numbers and the unit place is occupied with a digit(2,4 or 6).

Hundreds, tens place can be filled by remaining any 5 digits.

Therefore, there will be as many 2-digit numbers as there are permutations of 5 different digits taken 2 at a time.

Therefore, the required number of 2-digit numbers =^{5}P_2

                                                                           =\frac{5!}{(5-2)!}

                                                                            =\frac{5!}{3!}

                                                                           =\frac{ 5\times 4\times 3!}{3!}

                                                                         =5\times 4=20

Thus, by multiplication principle, required 3 -digit numbers is  3\times 20=60

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